I suppose after the BSG gripe it's only right that I detail one of my other whinges. My wife is more of a Cold Case fan than I am so I probably watch it more regularly than I otherwise would. My main problem with this show is not the odd suspension of suspension of disbelief but rather a structural problem to do with the way each narrative is handled.
The premise of the show to follow a particular murder Philadelphia PD's cold case team investigate and solve. This is portrayed by use of parallel narratives. As Lily Rush and her associates interview witnesses and suspects, their testimony flashbacks relate the story leading up to the murder. The first structural problem with this is that there's no particular reason for the stories to be synchronised. If you are piecing together the sequence of events up to a murder, it is surely more likely that these would arrive out of sequence.
The second structural problem is the narrative consistency of the flashbacks. The story is meant to be told by a series of individuals and yet appears as that of a single narrator. The depiction of character A by character B is consistent with his depiction by character C. This is particularly problematic when one of those interviewed inevitably turns out to be the perpetrator. You would think he would have a more self-serving narrative and be more inclined to send them on a wild goose chase and away from individuals who might possibly incriminate him. And yet, it's frequently the case that the eventual perpetrator provides them with the lead they need.
As far back as 1950, a solution was found to this problem. If Cold Case adopted a Rashomon-style format, it's hard to see what would be sacrificed. The flash-back story would have to be truncated as it would be told several times, from several viewpoints. But you would have a much more interesting storyline, and it would be much easier to accomodate the type of evasiveness and diversions you would imagine to characterise the testimony of people involved. Plus, the team would be forced to weigh and compare each person's testimony without assuming everyone to be telling the truth.